I did a lengthy calculation once involving Legendre and other
polynomials of high order (up in the 60s) and got remarkably accurate
results (IMHO, anyway).
However I discovered that it made an observable difference at high
enough orders whether the arguments were integers or reals. If the
arguments were reals I could see observable differences between the
results from two calculations that should theoretically have given
identical results; but if I entered an argument of 1.001 Pi in the form
1001 Pi/1000, for example, the results of the two alternative
calculations would agree exactly.